Intro to Centrality: Power and Prestige
Dan Cunningham
May 7, 2019
What is centrality?
- What is it
- The focus is on identifying “structurally advantageous” nodes.
- We often assume central indicates some form of “importance”.
- Why do we care?
- Well connected actors.
- Actors who are well connected and who are connected to other well connected actors.
- Potential brokers.
- Actors who may have access to a lot of other actors.
- Actors who are “flying under the radar”, so to speak.
- Potential emerging leaders.
Big Three + One (Undirected Data)
| Measure | Definition | Interpretation | Caveat |
|---|---|---|---|
| Degree (frequency) | Count of an actor’s ties. | Actor activity; Direct power or influence, or ability to be influenced by others | In some cases, well-connected actors are the result of biased connections. |
| Eigenvector (frequency) | Weights an actor’s degree centrality by the degree centrality of its neighbors. | Indirect influence or power; Potential social capital. | In well-connected networks (or sub- networks, such as cliques), it is often difficult to identify a single, or a few, potentially powerful actors. |
| Betweenness (paths) | How often each actor lies on the shortest path between all pairs of actors. | Brokerage potential; Gatekeepers; Boundary Spanners | Betweenness assumes a desire for efficiency. Actors, resources, and information may not always follow shortest paths. |
| Closeness (distance) | The average shortest path (i.e., geodesic) distance from an actor to every other actor in the network. | Actor levels of accessibility to others, and to material and non- material goods. | Not designed for use with disconnected networks. Pay close attention to program defaults and options for dealing with undefined distances. They can change how the results should be interpreted. |
Twitter Network Example
Sample of Accounts (Top 10 Based on Degree)
| Rank | Name | Tweet Count | #of Followers | Languages | Timeframe |
|---|---|---|---|---|---|
| 1 | zubovnik (113) | 5,014 | 25,144 | Many including English and Russian | Mid-2014 to Early-2018 |
| 2 | maxdementiev (84) | 4,969 | 102,052 | Many including English and Russian | Mid-2015 to Mid-2017 |
| 3 | novostispb (81) | 4,904 | 113,638 | Many including English and Russian | Mid-2015 to Mid-2017 |
| 4 | riafanru (71) | 22,886 | 12,948 | Many including English and Russian | Early-2015 to Mid-2017 |
| 5 | katka_hero (64) | 331 | 289 | Many including Russian | Mid-2015 to Early-2017 |
| 6 | emma_kvn (61) | 1,309 | 310 | Many including Russian | Early-2015 to Mid-2017 |
| 7 | margoberoeva (59) | 1,174 | 368 | Many including English and Russian | Mid-2015 to Mid-2016 |
| 8 | comradzampolit (56) | 9,596 | 41,004 | Many including English and Russian | Mid-2015 to Late-2017 |
| 8 | boeing_is_back (56) | 4,933 | 28,102 | Many including Russian | Mid-2015 to Late-2017 |
| 10 | thefoundingson (53) | 8,863 | 42,000 | Many including English and Russian | Late-2015 to Late-2017 |
Sample of Tweets
Twitter Network Example
Hypothetical Network (Offline)
Gang Network Statistics
Attribute Table (Gang Network Top-5 Eigenvector)
| Rank | Name | Affiliation | Other Gang Connections | Crime Type |
|---|---|---|---|---|
| 1 | O.G. (1) | County Boys | Almighty Angels,Blood Army, Guerrilla Posse, & 21st St. | Narcotic Offenses |
| 2 | Fat Boy (.07) | Almighty Angels | County Boys | Burglary |
| 3 | Freckles (.65) | Unknown | Almighty Angels & 21st St. | None |
| 4 | Boots (.62) | Unknown | Almighty Angels | None |
| 5 | 2 Tied at .56 | N/A | N/A | N/A |
Hypothetical Network (Offline)
YouTube Network Example
YouTube Network Statistics
YouTube Network Example
Central Account (Betweenness)
Select Comments
Heroin Distribution Network (NYC)
Heroin Distribution Network (NYC) Statistics
Heroin Distribution Network (NYC)
Centrality Comparison
Combinations of Centrality Measures
High Level Leaders
Emerging Leaders
Gatekeepers
Boundary Spanners
Centrality (Directed Networks)
Commonly Used Metrics
| Measure | Definition | Interpretation | Caveat |
|---|---|---|---|
| Indegree (frequency) | Count of direct incoming ties. | Highly sought after (resources, wisdom). | Accounts only for direct incoming ties, but not indirect relations. |
| Outdegree (frequency) | Count of direct outgoing ties. | Highly active; Distributor of material and/or nonmaterial goods. | Accounts only for direct outgoing ties, but not indirect relations. |
| Hubs and Authorities | A good hub is an actor that points to many good authorities, and a good authority is one that is pointed to by many hubs. | Major network connectors (hubs); Potential influence on network hubs (authorities). | Provides two scores (i.e., hubs and authority scores). Also, this algorithm provides same scores as Eigenvector when run on undirected networks. |
Indegree Centrality
Indegree Centrality
Outdegree Centrality
Outdegree Centrality
Hubs and Authorities
Questions?
